This randomized phase II trial studies how well ixazomib and dexamethasone or ixazomib, dexamethasone, and lenalidomide work based on the presence of the rearrangement of a gene called nuclear factor of kappa light polypeptide gene enhancer in B-cells 2 (NFKB2) in treating patients with multiple myeloma that has returned after a period of improvement or does not respond to treatment. Ixazomib may stop the growth of cancer cells by blocking enzymes called proteasomes needed for cell growth. Drugs used in chemotherapy, such as dexamethasone, work in different ways to stop the growth of cancer cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Lenalidomide may stimulate the immune system against cancer cells and may also prevent the growth of new blood vessels that tumors need to grow. It is not yet known whether ixazomib and dexamethasone, or ixazomib, dexamethasone, and lenalidomide are more effective in treating multiple myeloma.